The paper describes an approach for the identification of static nonlinearities from input-output measurements. The approach is based on a minimax approximation of memoryless nonlinear systems using Chebyshev polynomials. For memoryless nonlinear systems that are finite and continuous with finite derivatives, it is known that the error caused by the Kth order Chebyshev approximation in a specified interval is bounded by a quantity that is proportional to the maximum value of the (K+1)th derivative of the input-output relationship and decays exponentially with K. The described method identifies the system by first estimating the system output at the Chebyshev nodes using a localized linear model around the nodes, and then solving for the coefficients associated with the Chebyshev polynomials of the first kind.